Estimation Of Risk Premium Parameters In The Fisher Equation By The State Space Model And Kalman Filter: Case Of Turkey

Abstract

Statistical theories are universal and come into sight differently with respect to the conditions, time and societies. Therefore, the results obtained from an analysis should not be comprehended as valid for everywhere and in all conditions. A risk-increasing event in a country might have different effects in another country. What underlies the changefulness of interest rates as well as risk premiums is the expectation; thus the economical relations may have quite different appearances for various periods in different countries. In this study, the time-varying risk premium is attempted to be estimated using the Kalman filter and examining the term structure of the interests from the viewpoint of the Expectations Hypothesis (EH). Kalman filter approach takes the changefulness of interest rates, potentially permanent changes of risk premiums and overlapping errors of estimation into consideration. The study has used of the data on monthly interest rates (regarding the TL-based accounts) for the 2002:01-2018:10 period in Turkey’s economy. The most important feature of the study is that it allows us to identify how the factors causing changes in risk premiums for Turkey’s economy can be estimated in time using the Kalman filter with no predeterminations. According to the risk premium estimates obtained by using the Kalman filter, the risk premium takes positive values in some periods and negative values in other periods. The risk premium is estimated to be negative in high volatility periods and positive in low volatility periods. The results obtained provide rational investors with important and beneficial information about the uncertainties of future changes in the interest rates.

Keywords

• Expectation Theory
• risk premium
• estimation of time-varying parameters
• Kalman Filter.

Fisher Denklemindeki Risk Primi Parametresinin Durum Uzay Modeli Ve Kalman Filtresi İle Tahmini: Türkiye Örneği

Abstract

İktisadi teoriler evrensel olmakla birlikte koşullara, zamana ve toplumlara göre farklı görünümler alır. Bu nedenle yapılan bir analizden elde edilen sonuçların her yerde ve her koşulda geçerli olarak algılanmaması gerekir. Bir ülkede riski artıran bir gelişme başka bir ülkede aynı etkiyi yaratmayabilir. Gerek faiz oranlarındaki gerekse risk primindeki bu oynaklığın altında yatan şey beklentilerdir ki; ekonomik ilişkiler, farklı ülkelerde çeşitli dönemlerde oldukça değişik görünümler sergileyebilir. Bu çalışmada faizin vade yapısı Beklentiler Hipotezi (BH) açısından ele alınarak zamanla değişen risk primi Kalman filtresi kullanılarak tahmin edilmiştir. Kalman filtresi yaklaşımı, faiz oranındaki değişimlerin oynaklığını, risk primindeki olası kalıcı değişimleri ve üst üste gelen tahmin hatalarını dikkate almaktadır. Çalışmada Türkiye ekonomisine ait 2002:01-2018:10 dönemi için aylık faiz oranı (TL üzerinden açılan mevduatlara ilişkin faiz oranı) verilerinden yararlanılmıştır. Çalışmanın en önemli özelliği, Türkiye ekonomisi için risk primini değiştirmeye sebep olan faktörlerin zaman boyunca önceden belirlenmeksizin Kalman filtresi ile nasıl tahmin edeceğimizi sağlamasıdır. Kalman filtresi kullanılarak elde edilen risk primi tahminlerine göre, risk primi bazı dönemlerde pozitif, bazı dönemlerde ise negatif değerler almaktadır. Risk primi, oynaklığın yüksek olduğu dönemlerde negatif, oynaklığın düşük olduğu dönemlerde ise pozitif tahmin edilmiştir. Elde edilen tahmin sonuçları rasyonel yatırımcılara faiz oranlarındaki gelecek değişimlere ait belirsizlikler hakkında önemli ve yararlı bilgiler sunmaktadır.

Keywords

• Beklentiler Teorisi
• risk primi
• zamana göre değişken parametrelerin tahmini
• Kalman Filtresi

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